Attractors of Hopfield-type lattice models with increasing neuronal input

Abstract

<p style='text-indent:20px;'>Two Hopfield-type neural lattice models are considered, one with local <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula>-neighborhood nonlinear interconnections among neurons and the other with global nonlinear interconnections among neurons. It is shown that both systems possess global attractors on a weighted space of bi-infinite sequences. Moreover, the attractors are shown to depend upper semi-continuously on the interconnection parameters as <inline-formula><tex-math id="M2">\begin{document}$ n \to \infty $\end{document}</tex-math></inline-formula>.